Backstage at the St Barnabas community fete in Mile End Park, east London, a mood of mild panic has settled on Heavy Load, a band who like to style themselves as "Lewes' answer to the Ramones". The panic isn't really about how their set will be received, although it's hard not to feel that even the audience at St Barnabas - who have thus far been entertained by an eclectic line-up, including a jazz trio, a demonstration of Sikh martial arts, the late Ian Dury's former backing band the Blockheads and the local vicar singing I Fought The Law - are unprepared for Heavy Load's music, a foul-mouthed take on 60s garage punk so chaotic that even the band's members seem at a loss to describe it. "We sometimes say we sound like the Fall having a bare-knuckle fight with Bros," offers bass player Paul Richards, hopefully. It's more about the actual members of the band - or rather, the one missing member.

Heavy Load prefer not to advertise that three of their members - drummer Michael White, singer Simon Barker and guitarist Jimmy Nichols - have learning disabilities, partly because they want to be seen first as a band, not as disability advocates, and partly out of a certain up-yours punk rock spirit. "We want to let people work it out for themselves," Richards says. "I hate it at concerts when artists say, 'I'm sorry, I've got a cold' or something. You shouldn't make excuses for your performance. You should just get up there and do it."

Nevertheless, at St Barnabas, it's swiftly becoming clear that life in Britain's first disabled punk band brings unique challenges. White, who has Down's syndrome, has vanished. "Is he in the Portaloo?" asks guitarist Mick Williams. "Last time he went into a Portaloo before a gig, we couldn't get him out."

Barker, meanwhile, tries to calm his pre-gig nerves - he says he sometimes suffers seizures on stage due to flashing lights - by demonstrating his stage moves to his support worker. "Last night I did this," he says, throwing himself on his back and kicking his legs in the air. It's a dramatic move of which Iggy Pop would be proud, but Barker's support worker seems less impressed. He's an enthusiastic fan of the band, taking photographs for their website, but this is the third Heavy Load gig he's attended in as many days, and his expression is beginning to take on a definite hint of weariness. "Simon, the grass is wet," he says quietly but firmly. "I think you should get up."

And Nichols has spotted something that has piqued his interest more than Heavy Load's imminent gig - a passing Volkswagen Beetle - and has headed out of the backstage area to investigate further, his eyes hidden behind the enormous pair of wraparound sunglasses that he wears on stage. As Williams has noted, these make him look not unlike a member of the Velvet Underground, albeit a member of the Velvet Underground currently pursuing a Volkswagen Beetle through an east London community fete with a guitar slung around his neck.

"Jimmy!" shouts Richards, weakly. "Jimmy! Come back!"

It's a prime example of what the band's website cheerfully describes as "all the randomness that comes with The Load". As is underlined by Heavy Load: A Film About Happiness - a documentary that follows the band for two turbulent years and that recently won the Audience Award at the BritDoc Festival - Heavy Load seem to thrive in a state of perpetual mayhem that would cause any other band to throw in the towel. But then, as it swiftly becomes apparent, Heavy Load are not any other band. A few days before the St Barnabas fete, I meet them at a Brighton rehearsal studio. They have three gigs booked over the coming weekend, but don't seem particularly interested in rehearsing. They play two songs: a cover of Kylie Minogue's Can't Get You Out Of My Head that in Heavy Load's hands sounds catastrophic, like chucking-out time at a particularly rowdy pub, and one of their own called We Love George Michael, a hearty thumbs-up for the former Wham! frontman's sexual preferences: "We love George Michael," bellow Barker and Williams, more or less in unison, "because he's gay at weekends and gay in the week." When the song suddenly speeds up before crashing to an undignified halt, rehearsals seem to be over. "We don't really rehearse much," Williams says. "It destroys our spontaneity." You can't help feeling that this attitude may be a factor in their proud boast that, in 12 years, Heavy Load's music has "neither improved nor deteriorated".

They formed when Williams was employed by the Southdown Housing Association, a not-for-profit organisation that works with vulnerable people in Sussex. He discovered that Nichols, a Southdown tenant, played guitar and had "a love of going to pubs and seeing bands. We started chatting about putting a band together. We sent a memo round, and within a week we were rehearsing."

Richards, another Southdown worker, joined when their original bass player "fell off a bar stool and broke his arm". They settled on playing garage punk partly because of its simplicity - what nascent rock band hasn't fumbled their way through the Troggs' Wild Thing? - and partly because its anti-establishment stance accommodates Barker's unique vocal style. He has, as his support worker tactfully puts it, a tendency unexpectedly to shout out "inappropriate things", as I discover while trying to interview him. "I'll interview you," he interrupts. "How's your sex life?"

Besides, it's the only music on which the band members can agree. Williams and Richards like indie rock, White is a fan of both early rock'n'roll and, more unexpectedly, boybands including Blue and Westlife. Barker, meanwhile, says he likes Michael Bolton, Bros, George Michael, Rick Astley. "He's got some terrible records," Williams sighs sadly.

Perhaps understandably, their early live performances at disabled club nights generated a measure of controversy. "Some people really dug it and other people couldn't really understand what was going on," Richards says, a hint of pride in his voice. "We played at a Mencap event and they told us to turn it down. We played at my local community fete and divided the audience. The WI cake stall complained, which we took as a compliment."

"I suspect that, in the past, they've been given gigs as a kind of charitable act," says Jerry Rothwell, the director of Heavy Load: A Film About Happiness. "Then they'd start playing, come out with this stuff and people would either get it or leave very quickly." Whatever you think of Heavy Load's ramshackle, confrontational, obscenity-laden brand of rock, it certainly militates against charity, pity or any of the usual kneejerk reactions that disability provokes.

They received an unexpected boost two years ago, when Rothwell - best known for Deep Water, an acclaimed documentary about businessman Donald Crowhurst's attempt to compete in the 1968 Golden Globe round-the-world yacht race - began filming: "I came across this Mencap newsletter in my doctor's surgery," he says, "and there was this photo of a band with learning disabilities who did a version of I Fought The Law. I just thought, that's a great combination."

Uproariously funny and moving in equal measure, the documentary captures the band's attempts to record their debut album, perform in "mainstream venues" ranging from Nichols' local pub to the Wychwood Festival, and start their Stay Up Late campaign, which fights for people with learning disabilities' "right to party", frequently curtailed by their support workers' desire to clock off at 9pm. Equally gripping, it shows the band's ability to triumph over their own apparently perpetual state of disarray. Midway through filming, Williams leaves Sussex to begin a new life with his family in France (he now flies to Britain whenever Heavy Load have a gig). Meanwhile White, who Rothwell notes "has a huge ego that obviously the film fed", continually threatens to quit the band over musical differences. At one juncture, a particularly vicious row erupts over the merits of Westlife. "Michael said he hated me," says a shattered-looking Richards in its aftermath. "He said, 'I hate Paul Richards and I hate his beard.' "

The film's ongoing success has sent Heavy Load's career spiralling in a manner Williams describes as "ludicrous, quite outrageous". They have recorded a second album, Shut It, this time entirely of their own songs, based around Barker's utterances, some deeply prosaic (We're All In A Film), some flatly baffling (Is Bruce Forsyth Dead?). They're increasingly asked to play at mainstream venues, where they've been startled by the overwhelmingly positive audience reaction. "Initially you can see people have this look of horror, but by the end they're totally into it. I think they get off on the fun we have on stage."

The Stay Up Late campaign has garnered worldwide support, too. They recently played live in New York, an experience Barker describes as "all right" and Richards as "wild, better than I could have expected - all the things that could have gone wrong and none did." He thinks for a moment: "Apart from Simon saying 'piss' and 'bollocks' on live radio."

Nevertheless, a certain underlying tension is still detectable. While I'm with them, Heavy Load display an apparently bottomless capacity to bicker about music - the delicate subject of Westlife, for example, rears its ugly head on a couple of other occasions - and while White professes to be "a little bit happier", he still manages to announce his imminent departure. "I'm going to live in Los Angeles in America," he says, to baffled looks from his bandmates. "Actually, I'm going to do drama group, study acting, and after that I shall be a film star in Hollywood."

"I want to do my own band," White says, "and I'm still going to do that at the end of this year."

"The idea was you were going to try to do that and Heavy Load at the same time, right?" Richards frowns, before adding, "You're going to be the Phil Collins of Heavy Load. Hopefully, you'll be better than Phil Collins. I hate Phil Collins." And another row about music bursts into life.

It seems to have been resolved by the time they arrive in Mile End: two intervening gigs at a Liverpool disability festival went well and the mood is buoyant. The members are eventually rounded up and they take to the stage, performing a wild, flailing version of Bee Bop A Lula. As predicted, the audience reaction shifts from horror to bemusement to delight. Perhaps that's a result of the music's thrilling unpredictability: you genuinely have no idea what's going to happen next. Perhaps it's down to the infectious enthusiasm that spills off the stage. It's obvious that everyone in the band is having the time of their lives. And perhaps, as Richards said, "people just dig our sound".

Whatever the reason, the show ends in triumph. Enthused, the local priest runs on stage as their version of Wild Thing clatters to an earsplitting close. "Amazing!" he shouts into the microphone. "Praise The Load!" Backstage, the various members are swamped by fans. Barker runs around shaking everybody's hand, White liberally helps himself to the supply of free lager, and Williams finds himself being introduced to the lead singer of Sham 69.

Suddenly, there's a plaintive shout from Richards: "Has anyone seen Jimmy?" Peering past the well-wishers, he lets out a sound somewhere between a groan and a laugh. "I think Jimmy's still on stage."

And indeed he is, apparently oblivious to the fact that the rest of Heavy Load have long departed and the roadies are setting up the next band's equipment around him. Then again, he has every right to be there. After all, the crowd are still cheering. ·

· Heavy Load play the ICA in London on October 1 (details: 020-7930 3647, ica.org.uk). Heavy Load: A Film About Happiness is released on October 3 (heavyloadthemovie.com).